Question: Simplify to lowest terms. $\dfrac{16}{40}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 16 and 40? $16 = 2\cdot2\cdot2\cdot2$ $40 = 2\cdot2\cdot2\cdot5$ $\mbox{GCD}(16, 40) = 2\cdot2\cdot2 = 8$ $\dfrac{16}{40} = \dfrac{2 \cdot 8}{ 5\cdot 8}$ $\hphantom{\dfrac{16}{40}} = \dfrac{2}{5} \cdot \dfrac{8}{8}$ $\hphantom{\dfrac{16}{40}} = \dfrac{2}{5} \cdot 1$ $\hphantom{\dfrac{16}{40}} = \dfrac{2}{5}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{16}{40}= \dfrac{2\cdot8}{2\cdot20}= \dfrac{2\cdot 2\cdot4}{2\cdot 2\cdot10}= \dfrac{2\cdot 2\cdot 2\cdot2}{2\cdot 2\cdot 2\cdot5}= \dfrac{2}{5}$